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Questions and Answers
In calculating quartiles for a grouped continuous series, what is the formula to find the first quartile (Q1)?
For the given marks secured by students in an examination, what class interval is considered as the first quartile class?
When computing quartiles for discrete data, what is the value used to divide the total number of observations into four equal parts?
What is the term used to describe the value that just exceeds the corresponding class interval when finding the first quartile in cumulative frequencies?
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In computing quartiles for grouped continuous series, what does 'cf3' represent in the formula to find the third quartile (Q3)?
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When arranging ungrouped data to calculate deciles, what does 'Di' stand for in the formula 'Di = i(n+1)'?
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For ungrouped data, which formula is used to calculate Q1 quartile?
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In the context of quartiles, what is the significance of arranging data in increasing order?
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Which step is essential in finding Q3 for discrete data using cumulative frequencies?
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In grouped data - discrete series, what does 3(N+1) represent in quartile calculation?
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When computing quartiles for grouped data, what role do cumulative frequencies play?
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Why is it necessary to understand how to calculate quartiles in statistics?
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In a discrete data set, what does the first quartile (Q1) represent?
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For continuous data series, how is the lower boundary (S) of the lowest class calculated when finding the range?
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How is the second quartile (Q2) different from the other quartiles?
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When calculating quartiles for grouped data, what is used to determine Q1 and Q3?
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In a continuous data series, what does the third quartile (Q3) represent?
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How are quartiles helpful in analyzing a dataset?
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Study Notes
Quartiles
- Arrange the given data in increasing order to compute quartiles.
- For ungrouped data, use the formula: Q1 = (n+1)/4, Q2 = (n+1)/2, and Q3 = 3(n+1)/4.
- Example: For the data 25, 18, 30, 8, 15, 5, 10, 35, 40, 45, Q1 = 9.5, Q2 = 18, and Q3 = 36.25.
Quartiles for Grouped Data
- For discrete series, find cumulative frequencies (c.f) and total frequency (N).
- Use the formulas: Q1 = value just greater than N+1/4, and Q3 = value just greater than 3(N+1)/4.
- For continuous series, find cumulative frequencies (c.f) and total frequency (N).
- Use the formulas: Q1 = l1 + (h1/f1) * (N - cf1), and Q3 = l3 + (h3/f3) * (3N - cf3).
Deciles
- Deciles are the values that divide the total number of observations into 10 equal parts.
- There are 9 deciles, D1, D2, ..., D9.
- For ungrouped data, use the formula: Di = i(n+1)/10, where i = 1, 2, 3, ..., 9.
Relative Measure of Dispersion
- Relative measures of dispersion are free from the units of measurements of the observations.
- They are used to compare the variation in two or more sets with different units of measurement.
Measures of Dispersion
- Absolute measures: Range, Quartile Deviation, Mean Deviation, Standard Deviation.
- Relative measures: Co-efficient of Range, Co-efficient of Quartile Deviation, Co-efficient of Mean Deviation, Co-efficient of Variation.
Range and Co-efficient of Range
- Range = L - S, where L is the largest value and S is the smallest value.
- Co-efficient of Range = (L - S) / (L + S).
- For continuous series, use Method-I or Method-II to find L and S.
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Description
Learn how to compute quartiles for ungrouped data using formulas. Practice arranging data in increasing order and applying the formulas for Q1, Q2, and Q3 to find quartile values.
